Reactor control

In order to evaluate some of the possible advantages of hybrid reactors over critical reactors, we think useful to recall how these are controlled. This is essentially achieved by the motion of neutron absorbing control rods which modify the value of the criticality coefficient k_eff. Since the evolution of the reactor is determined by the ratio $\rho=\frac{1-k_{eff}}{k_{eff}}$, this quantity, called the reactivity, is used for discussing reactor control. The time constant associated to the motion of control rods is, typically, in the second range. The time delay $\tau_{nf}$ between two neutron generations is much smaller, typically 10^-7s for fast reactors and 10^-4s for thermal reactors[32]. Such numbers would imply a very fast evolution of the reactor even for very small positive reactivities. Let $k_{eff} ~=\frac{1}{1-\rho}~$ $\simeq1+\rho$ be the multiplying neutron coefficient after a reactivity change. The number of neutrons of the n^th generation neutrons is $(1+\rho)^{n}N_{0}$. It follows that the reactor power, which is proportional to the number of neutrons, increases exponentially with time t:

$$W(t)=W_{0}\exp\left( \frac{\rho t}{\tau_{nf}}\right)$$ (4.62)

Even for $\rho$=0.001 the power is multiplied by 2 after 8 neutron generations, i.e. 1 microsecond for fast reactors and 1 millisecond for thermal reactors! With such a fast rise in the reactor's power, one might think that reactor control by control rods would be hopeless. In fact the presence of a small fraction of delayed neutrons makes the things tractable.